First look for an approximate solution. Since the sinusoidal term is always
between , it is clear that a solution
is close to a solution of , which occurs when, now the term is identically zero
at that point, so this is an exact root.

That there are no other roots is obvious as the maximum rate of increase
of the middle term is less than (in fact it is )
so the entire LHS is a decreasing function and so the root is unique.